About The Mathematics Digital Library

The Mathematics Digital Library is a database of mathematics questions taken from textbooks and examination papers. It was founded in 2013 by Lee Chu Keong, for several reasons:

Reason No. 1: The Contents of Old Textbooks Remain Useful, But Are Usually Still Useful

Libraries spend huge amounts of money buying, cataloguing and making available textbooks. They buy these textbooks typically because an instructor in the university (or polytechnic, or some other type of learning institution) recommended it to his students. Typically, when the instructor leaves, or moves on to teach another subject, or finds a new textbook that catches his fancy, the old textbook is forgotten, i.e., it falls out of the radar of the instructor! Sometimes, the textbook is transferred to the “Closed Stacks” section of the library, and cannot even be found serendipitously by students.

The contents of the old textbook, however, remain as relevant as when it was first published! Understandably, students lack the time to explore these old textbooks (who has the time when a typical calculus textbook today is more than 700 pages long!), and they fail to benefit from the examples and exercises in them. Wouldn’t it be great if these examples and exercises were unlocked and made available to all?

Reason No. 2: Questions Are Recycled, Anyway

In my years of teaching, I have bought many mathematics textbooks (I actually collect them, and now I have plenty – mostly secondhand, and a few new ones). In fact, for some of the textbooks, I have multiple editions. Some examples of textbooks of which I have multiple editions:

Dennis D. Berkey’s Calculus — I have the first and second editions

George Thomas and Ross Finney’s Calculus and Analytic Geometry — I have the seventh, eighth and tenth editions

Howard Anton — I have the second, sixth and eight editions

Looking through the textbooks I have accumulated, I realised one thing — the questions in many textbooks have been recycled over and over again! As a result, there is frequently some degree of overlap between the questions from one textbook and those from another. In fact, the overlap between the questions from an edition of one book and those from other editions of the same textbook is often significant (in excess of 90%). The fact is that, at least for mathematics textbooks, authors recycle questions heavily. Wouldn’t it be great if these questions were made available to all in a central repository? For heavily recycled questions, see Example 1 and Example 2.

Reason No. 3: The High Cost of Textbooks

The cost of textbooks has been rapidly rising, and many students today have difficulty affording them (see this report to understand this problem better). I guess one reason for the high cost of textbooks is due to the huge number of pages (all or mostly printed in colour). Could the textbooks be thinned (and therefore made more affordable) by the removable of questions to a central repository? Wouldn’t it be great if authors could make references to questions from this central repository from the textbooks they write, and instead, concentrate on explaining mathematical concepts and proofs more clearly? This would be a revolution in how mathematics textbooks are written and published. Textbooks would be a lot “greener” too!

Reason No. 4: Huge Question Variety Aids Learning

This reason has to do with how students learn mathematics. Students learn mathematics more effectively if they are presented with questions that look alike and have solved in very different ways. To facilitate this, I have started a series of posts called “Compare and Contrast”, which collocates questions of this nature (see this example). Students also learn mathematics by drill, and this is best achieved by attempting questions that are alike in their solution process. I’ve attempted to do this with a series called “More or Less” (see this example).

Reason No. 5: No Database of Mathematics Questions

Currently, mathematics digital libraries already exist, but they cater to professional mathematics working at the postgraduate level. Examples of such digital libraries are: (1) European Digital Mathematics Library; (2) Russian Digital Mathematics Library; and (3) NIST Digital Library of Mathematical Functions. To the best of my knowledge, no database that caters to the engineering or science undergraduate that is learning mathematics. These students need questions for drill, but no database of mathematics questions exist. Such a database would be useful to a far larger audience than the above three databases.

Reason No. 6: Explanations Without Drill is Useless

Considerable efforts have gone into the creation of online videos to teach mathematics. Systematic collection of videos have been made available by the Khan Academy, and numerous individuals have posted ad hoc videos on YouTube. Mathematics, though, is not a spectator sport. Mastery requires the student to understand, imitate, and practice. These videos facilitate only the first of the three processes (understand). The Mathematics Digital Library provides sufficient questions for students to attempt and gain confidence (imitate and practice).

Reason No. 7: Local Content That Should Be International

Much mathematical content remains local, although they are useful internationally. One example are mathematics examination papers. I live in Singapore, and although Johor Bahru is just across the causeway, and there is much overlap in the mathematics syllabus of both countries, Singapore O- and A-Level examination papers cannot be purchased in Johor Bahru. There are three categories of local content:

So far, about 6,000 questions from old, out-of-print mathematics textbooks have been digitised. I have, where possible, included the source (or sources) from where I have obtained the question. As I am still formulating the “house style” for this database (or question bank), there is currently some unevenness about how the questions are presented.

If you’re an instructor, you can use the questions in your teaching. If you’re a student, for practice, and to prepare for your examinations. For researchers, you can study how mathematics has been taught (through the questions in the exercises).

The contents in this database will remain free.

If you with to contribute to The Mathematics Digital Library, you may do so in two ways:

(1) Work on the solutions. So far, only the questions have been keyed in as I have had no time to If you wish to work on the solutions (you will be acknowledged as the author of the solution), please email me at ascklee@ntu.edu.sg.

(2) If you have textbooks (particularly old, and difficult-to-find ones), please send them to me at: